Diferencia cuadrada de dos números consecutivos grandes

Dados dos números consecutivos positivos M y N, la tarea es encontrar la diferencia de cuadrados de los dos números sin calcular el cuadrado de esos números.
Ejemplos: 
 

Entrada: N = 4, M = 5 
Salida: 9 
Explicación: 
5 ² – 4 ² = 25 – 16 = 9.
Entrada: N = 999999999, M = 1000000000 
Salida: 1999999999 
 

Planteamiento: La idea es usar la expresión algebraica para resolver este problema. Se da en la pregunta que M = N + 1. Por lo tanto: 
 

• El valor a calcular es M ² – N ² .
• Al reemplazar M por N + 1, la ecuación anterior se convierte en: 
   

(N + 1)2 - N2

• (N + 1) ² se puede expandir a: 
   

N2 + 12 + 2 * N - N2

• Al simplificar, la ecuación anterior se convierte en:

1 + 2 * N
1 + N + N
(1 + N) + N
M + N

• Por lo tanto, simplemente necesitamos calcular y devolver el valor de M + N.

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ program to find the square
// difference of two large
// consecutive numbers
 
#include <bits/stdc++.h>
using namespace std;
typedef long long l;
 
// Function to find the square
// difference of two large
// consecutive numbers
l difference(l M, l N)
{
    return M + N;
}
 
// Driver code
int main()
{
    l M = 999999999;
    l N = 1000000000;
 
    cout << difference(M, N) << endl;
}

// Java program to find the square
// difference of two large
// consecutive numbers
 
 
class GFG{
  
// Function to find the square
// difference of two large
// consecutive numbers
static long difference(long M, long N)
{
    return M + N;
}
  
// Driver code
public static void main(String[] args)
{
    long M = 999999999;
    long N = 1000000000;
  
    System.out.print(difference(M, N) +"\n");
}
}
 
// This code is contributed by 29AjayKumar

# Python3 program to find the square
# difference of two large
# consecutive numbers
 
# Function to find the square
# difference of two large
# consecutive numbers
def difference(M, N):
    return M + N
 
# Driver code
if __name__ == '__main__':
    M = 999999999
    N = 1000000000
 
    print(difference(M, N))
 
# This code is contributed by mohit kumar 29   

// C# program to find the square
// difference of two large
// consecutive numbers
using System;
 
public class GFG{
   
// Function to find the square
// difference of two large
// consecutive numbers
static long difference(long M, long N)
{
    return M + N;
}
   
// Driver code
public static void Main(String[] args)
{
    long M = 999999999;
    long N = 1000000000;
   
    Console.Write(difference(M, N) +"\n");
}
}
 
// This code is contributed by 29AjayKumar

<script>
 
// JavaScript program to find the square
// difference of two large
// consecutive numbers
 
// Function to find the square
// difference of two large
// consecutive numbers
function difference(M, N)
{
    return M + N;
}
 
// Driver code
let M = 999999999;
let N = 1000000000;
 
document.write(difference(M, N));
 
</script>

1999999999